Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
399 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 399 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11771303 | C2 | semidirect |
| 5. C16×AGL(1,𝔽9) | C2 | semidirect |
| 21. #64218 | C8 | semidirect |
| 25. #64214 | C8 | semidirect |
| 28. #63773 | C8 | semidirect |
| 33. #63765 | C8 | semidirect |
| 35. C32×M32 | C8 | semidirect |
| 36. #63639 | C8 | semidirect |
| 37. #63625 | C8 | semidirect |
| 53. #3771 | C2×C8 | semidirect |
| 60. #3708 | C2×C8 | semidirect |
| 61. C32×C16 | C2×C8 | semidirect |
| 62. C3⋊(C3⋊C16) | C2×C8 | semidirect |
| 78. AGL(1,𝔽9) | M32 | direct (N × H) |
| 132. M32 | AGL(1,𝔽9) | direct (N × H) |
| 179. C16 | C2×AGL(1,𝔽9) | semidirect |
| 188. C32 | C8×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11795871 | 2 |
| M32×#157 | 2 |
| C2×C8×AGL(1,𝔽9) | 2 |
| #11771303 | 2 |
| C16×AGL(1,𝔽9) | 2 |
| C8×M32 | 9 |